POJ 3616 Milking Time（基础DP）

Milking Time

Description

Bessie is such a hard-working cow. In fact, she is so focused on maximizing her productivity that she decides to schedule her next N (1 ≤ N ≤ 1,000,000) hours (conveniently labeled 0..N-1) so that she produces as much milk as possible.

Farmer John has a list of M (1 ≤ M ≤ 1,000) possibly overlapping intervals in which he is available for milking. Each interval i has a starting hour (0 ≤ starting_hour_i ≤ N), an ending hour (starting_hour_i < ending_hour_i ≤N), and a corresponding efficiency (1 ≤ efficiency_i ≤ 1,000,000) which indicates how many gallons of milk that he can get out of Bessie in that interval. Farmer John starts and stops milking at the beginning of the starting hour and ending hour, respectively. When being milked, Bessie must be milked through an entire interval.

Even Bessie has her limitations, though. After being milked during any interval, she must rest R (1 ≤ R ≤ N) hours before she can start milking again. Given Farmer Johns list of intervals, determine the maximum amount of milk that Bessie can produce in the N hours.

Input

* Line 1: Three space-separated integers: N, M, and R
* Lines 2..M+1: Line i+1 describes FJ's ith milking interval withthree space-separated integers: starting_hour_i , ending_hour_i , and efficiency_i

Output

* Line 1: The maximum number of gallons of milk that Bessie can product in the N hours

Sample Input

12 4 21 2 810 12 193 6 247 10 31

Sample Output

43

定义dp[i]表示第i个时间段挤奶能够得到的最大值，即前面 i – 1个时间段任取0到i – 1个时间段挤奶，然后加上这个时间段的产奶量之和。dp[i]满足如下递推关系：

第i个时间段挤奶的最大值 = 前 i – 1 个时间段挤奶最大值中的最大值 + 第i次产奶量。

代码如下：

#include <cstdio>#include <algorithm>#include <cstring>using namespace std;const int maxm = 1005;typedef struct{int b;int e;int eff;}milk;milk mk[maxm];int dp[maxm];int cmp(milk a,milk b){return a.e < b.e;}int main(){int n,m,r,i,j,k;scanf("%d %d %d",&n,&m,&r);memset(dp,0,sizeof(dp));for(i = 0;i < m;i++){scanf("%d %d %d",&mk[i].b,&mk[i].e,&mk[i].eff);mk[i].e += r;}sort(mk,mk + m,cmp);for(i = 0;i < m;i++){dp[i] = mk[i].eff;for(j = 0;j < i;j++){if(mk[j].e <= mk[i].b){dp[i] = max(dp[i],dp[j] + mk[i].eff);}}}int maxmum = 0;for(i = 0;i < m;i++){if(maxmum < dp[i])maxmum = dp[i];}printf("%d\n",maxmum);return 0;}